It is no news that the COVID–19 pandemic has affected many persons in different ways. As the number of reported cases rises across the globe, efforts are geared towards production and administration of effective vaccines for the disease. However, many developing countries are faced with the dilemma of how to slow the spread and flatten the curves of the disease as the available vaccines are not enough. Interestingly, the dynamics of the disease can be analysed to get useful insights to enhance the making of suitable preventive policies that will slow the spread, ultimately flatten the curves of the disease and also help in managing any future occurrence. In this work, the aim is to analyse the dynamics, and estimate the basic reproduction number of the second wave of the pandemic in Nigeria using a Susceptible-Infected-Recovered-Deceased (SIRD) compartmental–based model. The dynamics of the disease is described by a system of nonlinear ordinary differential equations. The model takes into consideration the current control policies in place - social distancing, mask usage, personal hygiene and quarantine. Available data provided by Nigeria Centre for Disease Control (NCDC), World Health Organization (WHO) and Wolfram Data Repository were used for the computations. The Quasi–Newton algorithm was implemented in fitting the proposed model to the available data and a sensitivity analysis was presented. Major parameters - effective contact rate, average recovery time, average mortality rate, and overall effectiveness of the control policies - influencing the dynamics of the disease, and the basic reproduction numbers were estimated. The turning points of the disease during the second wave were also obtained. The proposed model gave estimated values for the parameters influencing the spread of the disease. Also, the measure of the overall effectiveness of the current control policies gave insight into how effective the measures are.